Convergence Theorems and Asymptotic Integration for Functional Differential Equations

This paper is devoted to the investigation on convergence of solutions and asymptotic integration of some functional differential equations FDEs.. In the first part of the paper, some convergence criteria are obtained, and an invariance principle is established for the convergence of solutions of linear FDEs under perturbations and disturbances with L1-integrable coefficients. These theorems are applicable to some nonlinear or nonhomogeneous equations. In the second part, the convergence theorems are applied to investigate the asymptotic integration of some linear FDEs. This research is made mainly to discuss a situation that was avoided by some previous literature. Some examples are given to illustrate the theorems.